More comprehensive methodologies have been proposed, which involve computing all pairwise inter-set distances between samples in \(\mathcal {C}\)  and \(\mathcal {G}\)  \((D_{\mathcal {C} \mathcal {G}} = [\texttt {dist}(c,g) : (c \in \mathcal {C}) \wedge (g \in \mathcal {G})])\) , as well as all pairwise intra-set distances for samples within a set \((D_{\mathcal {G} \mathcal {G}} = [\texttt {dist}(g_i,g_j) : (g_i \in \mathcal {G}) \wedge (g_j \in \mathcal {G}) \wedge (g_i \ne g_j)])\) . Note that we adapt the set-builder notation to construct a list (e.g., \([i/2 : 0 \le i < 4] = [0,0,1,1]\) ), which unlike a set, may contain duplicate values. CAEMSI [1]}, a domain independent framework for the analysis of SI systems, provides a statistical method to test the null hypothesis \(H_0 : (D_{\mathcal {G} \mathcal {G}} \ne D_{\mathcal {C} \mathcal {G}}) \vee (D_{\mathcal {C} \mathcal {C}} \ne D_{\mathcal {C} \mathcal {G}}) \vee (D_{\mathcal {C} \mathcal {C}} \ne D_{\mathcal {G} \mathcal {G}})\)  against the alternative hypothesis \(H_1 : D_{\mathcal {G} \mathcal {G}} = D_{\mathcal {C} \mathcal {C}} = D_{\mathcal {C} \mathcal {G}}\) . Yang and Lerch extract multi-dimensional features from each MIDI file [2]}. For each feature, \(D_{\mathcal {C} \mathcal {G}}\)  and \(D_{\mathcal {C} \mathcal {C}}\)  are constructed using Euclidean distance and smoothed using kernel density estimation [3]}, [4]}. The distance between \(D_{\mathcal {C} \mathcal {C}}\)  and \(D_{\mathcal {C} \mathcal {G}}\)  is measured using (1) the area of overlap and (2) the Kullback–Leibler Divergence [5]}. In contrast to both of these approaches, which involve evaluating the similarity between \(\mathcal {G}\)  and \(\mathcal {C}\) , StyleRank is optimized to evaluate the similarity of a single sample \(g \in \mathcal {G}\)  to \(\mathcal {C}\) .
